A simple proof?

Hi,

I was wondering if anyone can provide a proof for the following:

Let A, B, and C be three events with 0<=Pr(A)<=1, 0<=Pr(B)<=1, and
0<=Pr(C)<=1. Suppose that A carries positive information about C and B
carries positive information about C. Does it follow that that
intersection of AB carries positive information about C?

I'm thining that it does since AB is a subset of A and a subset of B, but I'm not positive. Any guidance is greatly appreciated!